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Ampleness equivalence and dominance for vector bundles. (arXiv:1706.07353v1 [math.AG])
来源于:arXiv
Hartshorne in "Ample vector bundles" proved that $E$ is ample if and only if
$\OOO_{P(E)}(1)$ is ample. Here we generalize this result to flag manifolds
associated to a vector bundle $E$ on a complex manifold $X$: For a partition
$a$ we show that the line bundle $\it Q_a^s$ on the corresponding flag manifold
$\mathcal{F}l_s(E)$ is ample if and only if $ \SSS_aE $ is ample. In particular
$\det Q$ on $\it{G}_r(E)$ is ample if and only if $\wedge ^rE$ is ample.\\ We
give also a proof of the Ampleness Dominance theorem that does not depend on
the saturation property of the Littlewood-Richardson semigroup. 查看全文>>